"Can" means able. "Cannot" (without a space between can and not) measns unable. I think the original poster wants to convey having the ability not to do something.
For example, "We cannot drink the water because it's contaminated with poison" means we are unable to drink the water; whereas, "We can not drink water and live for at least 3 days" means we are able to go without water for some time.
As another example, "I cannot exercise because I broke my ankle while skiing" means I am unable to exercise; whereas, "I can not exercise and still stay slim because I eat healthy" means I am able to stay slim while not exercising.
The original poster wanted a way to convey the ability to not do something using "can."
What do you think, everyone? Is this a proper distinction between "cannot" (without a space) versus "can not" (with a space)? Does anyone have a proper authority, for example, from a grammar or style book that describes this use of the term "can not"?